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Working set selection is a major step in decomposition methods for training least squares support vector machines (LS-SVMs). In this paper, a new technique for the selection of working set in sequential minimal optimization- (SMO-) type decomposition methods is proposed. By the new method, we can select a single direction to achieve the convergence of the optimality condition. A simple asymptotic convergence proof for the new algorithm is given. Experimental comparisons demonstrate that the classification accuracy of the new method is not largely different from the existing methods, but the training speed is faster than existing ones.

The importance of remanufacturing system has been extensively investigated in recent years. Taking into account the consumer valuation uncertainty and the demand uncertainty, this paper addresses the issue of closed-loop supply chain with remanufacturing by game theory. We consider two types of consumers in the market: loss-neutral consumers and loss-averse consumers. The lossneutral consumers are completely rational. The loss-averse consumers, on the other hand, are with losses being more painful than equal-sized gains being pleasant. When multichannel structure can be chosen, the manufacturer has three pricing strategies in direct market: (1) keeping the price high with a small discount, no customers choose the online store; (2) keeping the price high with a moderate discount, only the loss-neutral customers choose the online store; (3) keeping the price low with a big discount, all customers choose the online store. Consumers make up their decisive selections through comparing the price and channel attributes. We introduce utility function for analyzing the market demand and then identify the optimal pricing and channel strategy to maximize the manufacturer's profit. Finally, the rationality and validities of the proposed model are illustrated by numerical examples, and sensitivity analyses of the parameters are also presented.